A week into his second term, President Barack Obama is temporarily turning from perpetual political fights over the national debt, government borrowing, spending and taxing to tackle two other big issues: immigration and gun-law overhaul.

With Congress delaying a debt limit showdown until May 18, the White House postponing its annual budget submission until March and House Speaker John Boehner struggling to maintain Republican unity, this could be the time to strike.

National public opinion polls show a majority of Americans now support easing immigration laws and tightening federal gun restrictions.

That's not to say either fight will be easy. Both immigration and guns remain hot-button issues in Congress

The president met Monday with police chiefs from three towns that experienced mass shootings in 2012: Aurora, Colo.; Oak Creek, Wis., and Newton, Conn. "We recognize that this is an issue that elicits a lot of passion all across the country," Obama said.

He hopes public outrage over recent shootings strengthens his hand on curbing gun violence.

Meanwhile, a bipartisan Senate group Monday presented a new framework for overhauling the nation's immigration laws, including a path to citizenship for the 11 million illegal immigrants already here. Obama presses his case for immigration-law changes Tuesday in Las Vegas.

The White House also believes the political math of last November's election – in which Obama won overwhelming Hispanic support – helped soften GOP opposition to liberalizing immigration laws.

"What's changed, honestly, is that there is a new ... appreciation on both sides of the aisle – including maybe more importantly on the Republican side of the aisle – that we have to enact a comprehensive immigration reform bill," Sen. John McCain, R-Ariz., said Sunday on ABC.

Even so, the new Senate immigration proposal could face strong opposition in the Republican-controlled House.

And despite growing public support for gun curbs, the pro-gun lobby remains a potent force.